T-duality

T-duality is symmetry in string theory , applicable to type IIA and IIB string theories and two heterotic string theories. T-duality transformations act in spaces in which at least one region has the topology of a circle. With this transformation, the radius R of this region changes to 1 / R, and the “wound” states of the strings change to high-pulse string states in the dual theory.

For example, let's start with the IIA string, “wound” once around the area under consideration. According to T-duality, it will be displayed as a IIB string with a pulse in this area. A IIA string with a topological number (the number of revolutions around the region) equal to two (“wound” twice) will be displayed as a IIB string with a double pulse, etc.

The squared mass of a closed string is:

m^{2}={\frac {4N}{\alpha '}}+{\frac {n^{2}}{R^{2}}}+{\frac {w^{2}R^{2}}{\alpha ^{\prime 2}}}

{\ displaystyle m ^ {2} = {\ frac {4N} {\ alpha '}} + {\ frac {n ^ {2}} {R ^ {2}} + {\ frac {w ^ {2} R ^ {2}} {\ alpha ^ {\ prime 2}}}}

m ^ {2} = {\ frac {4N} {\ alpha '}} + {\ frac {n ^ {2}} {R ^ {2}} + {\ frac {w ^ {2} R ^ { 2}} {\ alpha ^ {{\ prime 2}}}}

invariant in exchange $R\leftrightarrow \alpha '/R,\quad n\leftrightarrow w$ ${\ displaystyle R \ leftrightarrow \ alpha '/ R, \ quad n \ leftrightarrow w}$ $R \ leftrightarrow \ alpha '/ R, \ quad n \ leftrightarrow w$ and the interactions and all other physical phenomena are also invariant, as can be shown. T-duality affecting D- branes changes their dimension by +1 or −1.

Andrew Strominger, Shin-Tung Yau and Eric Zaslow showed that mirror symmetry can be considered as T-duality applied to three-dimensional toroidal layers of Calabi-Yau space .

T-duality

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